Using a neural network to identify a stable region within a set of data?
If you're really just trying to find long contiguous flat regions in a sequence, you do not need machine learning. Your PI is mistaken. You would be better off simply writing a short data processing program. Your program could find the finite differences between adjacent datapoints, and then count whether a long string of them are below some threshold to identify long flat regions. This will be faster, simpler, and perhaps more accurate than using ML on data visualizations for this task.

If you are trying to find something more complex than these long flat regions, you could instead train an LSTM on the raw sequential data that you are using to generate the images. Again, that will probably be more accurate than trying to train a CNN, or any non-sequential model, on the image data itself.